Question Number 66468 by mathmax by abdo last updated on 15/Aug/19 $${calculate}\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dx}}{\left({x}^{{n}} \:+\mathrm{3}\right)^{\mathrm{2}} }\:\:{with}\:{n}>\mathrm{1} \\ $$ Commented by mathmax by abdo last…
Question Number 933 by 123456 last updated on 29/Apr/15 $${f}\left({x}\right)=\frac{\mathrm{ln}\:{x}}{{x}} \\ $$$$\underset{\mathrm{1}} {\overset{{e}} {\int}}\:\frac{{f}\left({x}\right)}{{x}}{dx}=? \\ $$$$\:\underset{\mathrm{1}} {\overset{{e}} {\int}}\frac{\mathrm{ln}\:{f}\left({x}\right)}{{x}}{dx}=? \\ $$ Commented by prakash jain last…
Question Number 66466 by mathmax by abdo last updated on 15/Aug/19 $${find}\:\:{f}\left({a},{b}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{cos}\left({ax}\right){cos}\left({bx}\right)}{\left({x}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)\left({x}^{\mathrm{2}} \:+{b}^{\mathrm{2}} \right)}{dx}\:\:{with}\:{a}>\mathrm{0}\:{and}\:{b}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left({x}\right){cos}\left(\mathrm{2}{x}\right)}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+\mathrm{4}\right)}{dx} \\…
Question Number 132000 by bramlexs22 last updated on 10/Feb/21 $$\:\mathrm{super}\:\mathrm{nice}\: \\ $$$$\:\int_{\mathrm{0}} ^{\infty} \left(\frac{\mathrm{1}}{\left(\mathrm{x}^{\mathrm{3}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} }\right)^{\mathrm{2}} }\:\right)\mathrm{dx} \\ $$ Answered by EDWIN88 last updated on…
Question Number 66465 by mathmax by abdo last updated on 15/Aug/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{2}{i}\right)\left(\:{x}^{\mathrm{2}} \:+\mathrm{4}{j}\right)}\:\:\:{with}\:{i}={e}^{\frac{{i}\pi}{\mathrm{2}}} \:{and}\:{j}={e}^{{i}\frac{\mathrm{2}\pi}{\mathrm{3}}} \\ $$ Commented by mathmax by abdo last…
Question Number 66464 by mathmax by abdo last updated on 15/Aug/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{3}\right)\left({x}^{\mathrm{2}} +\mathrm{8}\right)^{\mathrm{2}} } \\ $$ Commented by mathmax by abdo last…
Question Number 66459 by mathmax by abdo last updated on 15/Aug/19 $$\left.\mathrm{1}\right)\:{calculate}\:{by}\:{residus}\:{method}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{3}} } \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{1}+{x}^{\mathrm{4}} }{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{3}} }{dx} \\ $$…
Question Number 131991 by mnjuly1970 last updated on 10/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:\:\:\:\:\:\:\:{calculus}…\:\: \\ $$$$\:\:{prove}\:\:{that}\:: \\ $$$$\:\:\phi_{\mathrm{1}} =\int_{\mathrm{0}} ^{\:\mathrm{1}} {li}_{\mathrm{2}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)=\frac{\pi^{\mathrm{2}} }{\mathrm{2}}\:−\mathrm{4} \\ $$$$\:\:\:\:\phi_{\mathrm{2}} =\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{log}\left(\mathrm{1}−{t}\right)}{{t}^{\frac{\mathrm{3}}{\mathrm{4}}}…
Question Number 66446 by ~ À ® @ 237 ~ last updated on 15/Aug/19 $$\:\:{Find}\:\:\:\:\int_{\mathrm{1}} ^{\infty} \:\left(\frac{\mathrm{1}}{{E}\left({x}\right)}\:−\frac{\mathrm{1}}{{x}}\right){dx} \\ $$ Commented by mathmax by abdo last…
Question Number 907 by Yugi last updated on 19/Apr/15 $${Determine}\:{the}\:{results}\:{of}\:{the}\:{following}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{I}_{\mathrm{1}} =\int\sqrt{\frac{{a}+{e}^{{x}} }{{a}−{e}^{{x}} }}{dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{I}_{\mathrm{2}} =\int\frac{\left({tanx}\right)\mid{tanx}\mid}{\mathrm{1}−{tan}^{\mathrm{2}} {x}}{dx} \\ $$ Commented by prakash jain…